Question

A ledder kept inclined at an angle of 40 degree at a distance of 8 feet from the building touches the building at some height.If the same ladder is kept at a distance of 6 feet with an inclination of 50 degree then find the height at which the ladder touches the building.

Answer 1

If a ladder is at an inclination of 40 deg with a distance of 8 feet or if the distance is kept to 6 feet with inclination of 50 deg then the height at which the ladder touches the building is 7.15 feet.

Step-by-step explanation:

Case 1:

Let the height at which the inclined ladder at an angle of 40° with the ground, touches the building be “h” feet. (As shown in the figure below).

Distance between the foot of the ladder and the building = 8 feet

According to the right-angled trigonometric ratio, we have

tan θ = (height of the building) / base

⇒ tan 40° = h / 8  

⇒ h = 8 * 0.839 = 6.712 feet ….. (i)

Case 2:

Let the height at which the inclined ladder at an angle of 50° with the ground, touches the building be “(h + x)” feet. (As shown in the figure below).

Now, the distance between the foot of the ladder and the building = 6 feet

According to the right-angled trigonometric ratio, we have

tan θ = (height of the building) / base

⇒ tan 50° = (h+x) / 6

⇒ h+x = 6 * 1.191

⇒ h + x = 7.15

⇒ x = 7.15 - 6.712 ...... [from (i)]

⇒ x = 0.438 feet

∴ h + x = 6.712 + 0.438 = 7.15 feet

Thus, the height at which the ladder touches the building is 7.15 feet.

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Answer 2

A ladder kept inclined at an angle of 40 degree at a distance of 8 feet from the building touches the building at height 6.7 ft and when ladder kept inclined at an angle of 50 degree at a distance of 6 ft from the building touches the building at height 7.2 ft

Step-by-step explanation:

In first case

Let height at which ladder touches the building=x

$\theta=40^{\circ}$

$BD=8 ft$

$tan\theta=\frac{perpendicular\;side}{base}$

$tan 40=\frac{x}{8}$

$x=8tan 40=6.7$ft

In second case

Let height at which ladder touches the building=y

$\theta=50^{\circ}$

$BC=6 ft$

$tan50=\frac{y}{6}$

$y=6tan50$

$y=7.2 ft$

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https://brainly.in/question/2059288 Solved by Bhagyashree chowdhry